Fulham have already released Marek Rodak, Tyrese Francois and Terence Kongolo, while Tosin Adarabioyo will officially join Chelsea on July 1 after deciding against renewing his deal with the Cottagers.
Like Adarabioyo, Willian and De Cordova-Reid are both coming towards the end of their contracts, with their current deals set to expire at the end of the month.
Fulham have allegedly offered Willian a one-year deal, while they have presented De Cordova-Reid with a two-year contract offer.
Fulham set to bid farewell to Willian, De Cordova-Reid
However, according to The Evening Standard, Willian and De Cordova-Reid are yet to agree new deals and will become free agents when their contracts run out.
The report claims that Fulham have not given up hope and are willing to continue negotiations even after their contracts come to an end.
Last year, Willian allowed his contract to run out before he eventually returned to Craven Cottage on a fresh one-year deal.
Twelve months on, the 35-year-old has been linked with a potential move to Saudi Arabia, while there is also thought to be interest from clubs in Brazil.
Meanwhile, De Cordova-Reid is likely to delay any decisions over his future until he has finished representing Jamaica at Copa America 2024.
How could their departures affect Fulham?
If they are unable to agree new contracts, Fulham will bid farewell to two players who have been regular fixtures in Marco Silva's side.
De Cordova-Reid registered six goals and two assists in 33 Premier League matches last season, while Willian scored four goals and provided two assists in 31 top-flight appearances.
The pair's departures will leave Silva with Adama Traore, Harry Wilson and Alex Iwobi as their main wide options for the 2024-25 season.
As a result, Fulham would have to delve into the transfer market to bring in replacements in what could be a busy transfer window for the Cottagers.
They are already looking for a new centre-back and striker, and they may need to find a new central midfielder if Joao Palhinha is sold this summer.
Palhinha is continuing to attract interest from Bayern Munich, but the German giants are yet to meet Fulham's £60m asking price.